The studies listed were from the 1982 and 1984, and I was wondering if any more thorough research has been conducted since, or whether the US really scrutinized the effect of radiation fallout over the town from their own tests.
I'm a little confused as to your title — atmospheric nuclear testing (which is what spreads fallout) stopped in the US in 1962, prior to the Limited Test Ban Treaty going into effect. So there weren't any atmospheric testing going on in the US when the Chernobyl accident happened. Cancers from radiation exposure can take decades to manifest. There certainly were studies of how fallout exposure harmed Americans though many of those came only in the post-Cold War; I don't think one can point some kind of arrow between Chernobyl (a reactor accident) and those studies (people had been concerned about fallout since the 1950s).